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Combined lp and quasi-Newton methods for minimax optimization

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Abstract

We present an algorithm for minimax optimization that combines LP methods and quasi-Newton methods. The quasi-Newton algorithm is used only if an irregular solution is detected, in which case second-order derivative information is needed in order to obtain a fast final rate of convergence. We prove that the algorithm can converge only to a stationary point and that normally the final rate of convergence will be either quadratic or superlinear. The performance is illustrated through some numerical examples.

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Authors and Affiliations

  1. Technical University of Denmark, Lyngby, Denmark

    Jørgen Hald & Kaj Madsen

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  1. Jørgen Hald
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  2. Kaj Madsen
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Hald, J., Madsen, K. Combined lp and quasi-Newton methods for minimax optimization. Mathematical Programming 20, 49–62 (1981). https://doi.org/10.1007/BF01589332

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  • DOI: https://doi.org/10.1007/BF01589332

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